Demand uncertainty and learning in fuzziness in a continuous review inventory model

This paper presents a continuous review inventory model with backorders and lost sales with fuzzy demand and learning considerations. The imprecision in demand is characterized by triangular fuzzy numbers. The triangular fuzzy numbers, counts upon lead time, are used to construct fuzzy lead time demand. It is assumed that the imprecision captured by these fuzzy numbers reduce with time because of learning effect. This implies that the decision maker gathers information about the inventory system and builds up knowledge from the previous shipments. Learning process occurs in setting and estimating the fuzzy parameters to reduce errors and costs. Under these considerations, the proposed model offers a policy and a solution algorithm to calculate the number of orders and reorder level such that the total annual cost attains a minimum value. The results of the proposed model are compared with the continuous review inventory system with fuzzy demand with or without learning effect. It is shown that learning effect in fuzziness reduces the ambiguity associated with the decision making process. Finally, numerical examples are provided to illustrate the importance of using learning in fuzzy model. The convexity of the total cost function is also proved.